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An Intrinsic Framework for Analysis of Facial Surfaces

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Abstract

A statistical analysis of shapes of facial surfaces can play an important role in biometric authentication and other face-related applications. The main difficulty in developing such an analysis comes from the lack of a canonical system to represent and compare all facial surfaces. This paper suggests a specific, yet natural, coordinate system on facial surfaces, that enables comparisons of their shapes. Here a facial surface is represented as an indexed collection of closed curves, called facial curves, that are level curves of a surface distance function from the tip of the nose. Defining the space of all such representations of face, this paper studies its differential geometry and endows it with a Riemannian metric. It presents numerical techniques for computing geodesic paths between facial surfaces in that space. This Riemannian framework is then used to: (i) compute distances between faces to quantify differences in their shapes, (ii) find optimal deformations between faces, and (iii) define and compute average of a given set of faces. Experimental results generated using laser-scanned faces are presented to demonstrate these ideas.

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Authors and Affiliations

  1. Department of Mathematical Engineering, Catholic University of Louvain, Bâtiment Euler (A.202), Avenue Georges Lemaitre 4, 1348, Louvain-la-Neuve, Belgium

    Chafik Samir

  2. Institut TELECOM, TELECOM Lille1 LIFL UMR 8022, Rue G. Marconi, Cité Scientifique 59650, Villeneuve d’Ascq, France

    Mohamed Daoudi

  3. Department of Statistics, Florida State University, Tallahassee, FL, 32306, USA

    Anuj Srivastava

  4. Department of Mathematics, Florida State University, Tallahassee, FL, 32306, USA

    Eric Klassen

Authors
  1. Chafik Samir
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  2. Anuj Srivastava
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  3. Mohamed Daoudi
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  4. Eric Klassen
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Correspondence to Chafik Samir.

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Samir, C., Srivastava, A., Daoudi, M. et al. An Intrinsic Framework for Analysis of Facial Surfaces. Int J Comput Vis 82, 80–95 (2009). https://doi.org/10.1007/s11263-008-0187-8

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  • DOI: https://doi.org/10.1007/s11263-008-0187-8

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